Firstly, yeah, the apology letter is a joke. It's intended to be over-the-top for a nothing situation. This is in the style of a pretty well-known apology in Japanese media, but that's niche and would take too long to explain, so I won't bother with that. The original panel is real, although it's since been deleted from the internet. The apology letter and image of Kana has, similarly, been deleted from the internet. Which makes this upload possibly the only version of this available online in any language.
And to give a bit more context, the idea of "a yuri manga" tends to have connotations of purity to it, and seeing a protagonist suddenly pull such a strange face in a yuri manga might be jarring. But the editor is essentially suggesting (in my opinion) that the readers are expecting a gag manga, the yuri part being secondary.